I was talking to my girlfriend, IrishGirl (@irishgirl31 on Twitter), about the now famous (or is it infamous?) Monty Hall problem:
Contestants on a game show are given the choice of three doors: behind one door is a car; behind the others, goats. After a contestant picks a door, the show’s host, who knows what's behind all the doors, opens one of the previously unopened doors, which reveals a goat. He then asks the contestant, "Do you want to switch doors?" Should the contestant switch doors?
If you haven’t heard about it or read about it you should, Jeff Atwood has a great overview or go to the source Marilyn vos Savant -- wow I bet a lot of those PhDs and math professors wish she’d take down their quotes! Wouldn’t it be fun to take a class from James Rauff, Ph.D., Professor of Mathematics at Millikin University who said:
I have been a faithful reader of your column, and I have not, until now, had any reason to doubt you. However, in this matter (for which I do have expertise), your answer is clearly at odds with the truth.
and just heckle the hell out of him for being totally WRONG about this? Okay I shouldn’t pick on James… the exalted Paul Erdos didn’t believe the right answer either until a colleague wrote a computer simulation to prove it to him (Hmmm… that sounds fun actually, I think I might write a computer simulation in my spare time tonight).
To me the whole issue is an amazing study in how poor humans really are at understanding probabilities. Casinos know this fact VERY well and I’m sure this human flaw is a major reason casinos do so well, even in a down economy. People throw good money over bad in hope that the odds are NOW magically in their favor! Sorry chump doesn’t work that way!
Anyway I didn’t want this post to be a re-re-re-rehash of the original problem I really just wanted to say that it was a very nice intellectual conversation working through the Monty Hall problem with IrishGirl… because as I’ve learned you can’t truly explain something to someone else if you don’t fully understand it yourself. It took about fifteen minutes to convince her that you should ALWAYS change your initial choice after the host reveals the goat. Always. You will win 66% of the time if you switch and only 33% of the time if you don’t. Hurts the brain, huh?
All of this talk reminded me of how much I truly enjoy problem solving, logic, probability and statistics. I’m not very good at any of those things but I do enjoy having my mind bent on occasion. I’m not sure why but this simple logic problem has always stuck in my head. Yes I was actually asked this question back in the early ‘90s when I interviewed at Microsoft (it was a series of 6 hour long interviews to go from being an “a-“ to a “blue badge”). The answer is very simple but it makes you think a bit and you don’t need to draw a chart to solve it - and I guess that’s why I like it.
There are three sets of marbles: all white, all black, and mixed white & black
There are three velvet bags (think Crown Royal – as in you cannot see through them)
Each bag has a label attached to it: White, Black, or Mixed
Each bag contains one set of marbles
The labels on the bags are guaranteed to be incorrect
How many marbles do you need to pull to correctly re-label the bags? Explain your answer.